Totally agree here - it might be from the hand sanitizer, which is not meant to be used on the genitals.
And yes - did you use a condom?
Go get a doctor to look at the sore. It may need treatment. If you didn't use a condom, get them to swab it.
Since the red spot appeard the next day it would not be std related as symptoms take a few days. sounds more like an irritation from the act itself. Did you use a condom?
It's now a wet sore for about 3 days*